The theoretical and experimental results of an investigation into the effect of the space charge of the ions on the frequency of the free axial oscillations in an isochronous cyclotron are discussed. The frequency of the axial oscillations was determined by using an external electric field to excite a resonance of the free oscillations. It is shown that the axial oscillation frequency varies with the space charge density in accord with the theoretical predictions. The azimuthal extent of the bunch of accelerated particles has been determined experimentally at various radii. The work was carried out at the Laboratory for Nuclear Problems at the Joint Institute for Nuclear Research on a cyclotron with an azimuthal magnetic field variation.